Question

The endpoints of the directed line segment AB are A(−7, 4) and B(8, 9). Find the coordinates of point P along line segment AB so that the ratio of AP to PB is 2 to 3. pls help

Answer 1

(-1,5)

Explanation:

When a line segment is divided in the ratio m:n, we use the section formula to determine the point P which divides the line segment:

The coordinates of x and y are:

`(x,y)=\left((mx_2+nx_1)/(m+n), (my_2+ny_1)/(m+n)\right)`

Given:

`A(x_1,y_1)=(-7, 4)\\B(x_2,y_2)=(8, 9)\\AP:PB=m:n=2:3`

The coordinates of P is:

`(x,y)=\left((2*8+3*-7)/(2+3), (2*9+3*4)/(2+3)\right)\\=\left((-5)/(5), (25)/(5)\right)\\\\=(-1,5)`